I plan on smoking different types of meat (pork, poultry and beef) together. I have a vertical smoker with a water pan in it. If i was to use 3 different flavors of seasoning/rubs will the flavors combine a bit from the drippings mingling in the water/drip pan and then affect the overall results?

I don't think that will be a problem. I never thought I got much of an affect as far as flavor goes from seasonings in a water pan. In fact I no longer put water in my pan. Just foil to make cleanup easier.

First: put your poultry on the bottom as you don't want that dripping on the other meats.
You will get some seasoning dripping down and there is a debate over which is better; beef dripping on pork or pork dripping on beef. As far as the water pan goes, I don't think you will notice any change in flavor from that but then I haven't used a water pan in years.
Why not? It takes more charcoal to get the water hot.

Why not put water in it? Does it not have that much affect on the moisture of the meats? I did brine my first attempt (pork loin), id that enough to keep it moist?

I don't use it because I didn't find any noticeable difference when I cooked without water in the pan. And there was less mess to clean up after the smoke. With proper technique and temp control meat won't get dry even without water in the pan. I also think you will find you get crispier skin on poultry and better bark on beef and pork without water.

I also do not use the water pan in the smokers that I have. In fact I fill mine with sand and cover with foil. This creates a thermal mass that helps the smoker with temp swings. This is especially useful when smoking in crappy weather.